Multiple antenna (MIMO) technologies have become commonplace in wireless communications systems in order to provide spatial diversity and improve performance and/or provide spatial multiplexing and increase the transmitted data rate. For instance, mobile WiMAX systems employ two MIMO profiles on the downlink:
Matrix A: This is the well-known Alamouti space-time code (STC) for transmit diversity described in S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications,” IEEE Journal on Selected Areas in Communications, vol. 16, no. 8, pp. 1451-1458, October 1998. This MIMO scheme provides diversity, but it has no spatial multiplexing gain. Although 2 transmit antennas are used, the transmitted data rate is the same as in single antenna systems. The virtue of this technique is that it provides a transmit diversity order of 2. With N antennas at the receiver, the total diversity order is 2N. Therefore, with 2 receive antennas, it leads to 4th-order diversity.
Matrix B: This scheme is based on spatial multiplexing (SM) of two data streams transmitted by the two transmit antennas. SM does not provide any diversity on the transmitter side, but, with N antennas at the receiver and maximum-likelihood detection (MLD), it provides a diversity order of N. In other words, second-order diversity can be achieved with 2 receive antennas.
There are also more advanced 2×2 MIMO schemes providing better diversity/multiplexing tradeoffs. These include the Golden code, in J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The Golden Code: A 2×2 Full-Rate Space—Time Code with Nonvanishing Determinants,” IEEE Transactions on Information Theory, Vol. 51, No. 4, pp. 1432-1436, April 2005, which is the best known STC of dimension 2×2, or the recently proposed STC, in the European Patent Application, EP 07 290 394.1, which provides similar performance to the Golden code while simplifying the optimum detector by orders of magnitude. The STC in said patent application is described by the coding matrix:
                              D          =                      [                                                                                                      as                      1                                        +                                          bs                      3                                                                                                                                  -                                              cs                        2                        *                                                              -                                          ds                      4                      *                                                                                                                                                              as                      2                                        +                                          bs                      4                                                                                                                                  cs                      1                      *                                        +                                          ds                      3                      *                                                                                            ]                          ,                            (        1        )            where a, b, c, and d are complex-valued design parameters and the star designates complex conjugate.
In this matrix representation, the first column represents the symbol combinations transmitted during a first symbol interval and the second column represents the symbol combinations transmitted during the second symbol interval. The first row of the matrix gives the symbol combinations transmitted from the first transmit antenna, and the second row of the matrix gives the symbol combinations transmitted from the second antenna. As described in said patent application, the complexity of the maximum likelihood (ML) decoder of this code is proportional to M2, where M is the size of the signal constellation.
To further increase the spatial multiplexing and the diversity gains, future standards will include MIMO systems with a larger number of antennas, for instance 4×4 MIMO schemes. There are many well-known STC designs for this type of systems. The simplest one is the pure spatial multiplexing scheme, which consists of transmitting in parallel 4 data streams using the 4 transmit antennas. Another one is the Double Alamouti scheme, which consists of transmitting one Alamouti matrix from the first two antennas and another Alamouti matrix in parallel from the other two antennas. This scheme offers a multiplexing gain of 2 (compared to 4 in the SM case), but its diversity order is 8 instead of 4 in the SM technique. More generally, one can design an STC providing a multiplexing gain of 4 and leading to high diversity and coding gains, but the complexity of the optimum decoder would be excessive for practical applications.                When the size of a MIMO system is increased, for instance by a factor 2 for upgrading a K×K MIMO system into a 2K×2K MIMO system, the complexity, or the computation load, is increased by a large factor. Consequently, more costly technologies need to be used. Furthermore, these technologies imply higher power consumption, thus causing an increased need for cooling the integrated circuits. The total cost is thus quite impacted.        